After captain Darren Sammy won the toss and elected to bat, the tourists were all out for 70 off 23.5 overs, their third lowest total behind 54 against South Africa in 2004 and 61 against Bangladesh in 2011.
Four West Indian batsmen were dismissed for ducks with only Darren Sammy (16), Keiran Powell (11) and Darren Bravo (11) making it into double figures.
Clint McKay started the rot when he removed former captain Chris Gayle (four), but it was Starc who did the majority of the damage to finish with figures of five for 20.
James Faulkner (two for 14 off five overs) took a wicket with his fifth delivery in ODI cricket when he removed Dwayne Bravo for a duck and was able to finish off the work of his fellow left-armer Starc.
Faulkner's dismissals came from identical deliveries that angled across right-handers to take the outside edge and find first slip Michael Clarke, who snaffled three in the cordon.
Starc followed up McKay's opening blow by dismissing Powell with a perfect outswinger to a left-hander, then had Ramnaresh Sarwan bowled with another swinging delivery through gate two balls later.
When Starc dismissed Dwayne Bravo and Kieron Pollard both for ducks in his fourth, the visitors had fallen to 19 for five having lost four wickets for just one run.
Pollard had survived a big LBW shout, which was reviewed with just more than half the ball being shown to be missing the stumps before he played on with an expansive drive.
Captain Darren Sammy and debutant Jason Holder (seven) led a brief revival when they combined for a 26-run partnership before McKay returned to the attack to remove Sammy. McKay then had Sunil Narine caught behind before chief destroyer Starc returned to knock over Jason Holder when he played a flamboyant looking drive.